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Relations and Functions

Each subtopic includes About section, revision page link, 10 preview questions, and practice CTAs.

Types of Relations: Reflexive, Symmetric, Transitive and Equivalence

Subtopic

Types of Relations: Reflexive, Symmetric, Transitive and Equivalence under Relations and Functions for Grade 12 ICSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    If a relation R={(1,1),(1,2),(2,2)}R = \{(1, 1), (1, 2), (2, 2)\} is defined on the set A={1,2}A = \{1, 2\}, then the relation RR is:

    A.

    Symmetric only

    B.

    Reflexive and Transitive but not symmetric

    C.

    An equivalence relation

    D.

    None of these

  2. 2.

    Let A={x,y,z}A = \{x, y, z\}. The identity relation IA={(x,x),(y,y),(z,z)}I_A = \{(x, x), (y, y), (z, z)\} defined on set AA is an:

    A.

    Equivalence relation

    B.

    Only reflexive relation

    C.

    Only symmetric relation

    D.

    Only transitive relation

  3. 3.

    In the context of relations on a set AA, a relation RR is defined to be transitive if:

    A.

    (a,b)∈R(a, b) \in R and (b,a)∈R  ⟹  a=b(b, a) \in R \implies a = b

    B.

    (a,b)∈R(a, b) \in R and (b,c)∈R  ⟹  (a,c)∈R(b, c) \in R \implies (a, c) \in R

    C.

    (a,a)∈R(a, a) \in R for every a∈Aa \in A

    D.

    (a,b)∈R  ⟹  (b,a)∈R(a, b) \in R \implies (b, a) \in R

Download the worksheet for Relations and Functions - Types of Relations: Reflexive, Symmetric, Transitive and Equivalence to practice offline. It includes additional chapter-level practice questions.

Types of Functions: One-to-one and Onto functions

Subtopic

Types of Functions: One-to-one and Onto functions under Relations and Functions for Grade 12 ICSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Let f:[0,π]→[−1,1]f: [0, \pi] \rightarrow [-1, 1] be defined by f(x)=cos⁡xf(x) = \cos x. This function is:

    A.

    One-to-one and onto

    B.

    One-to-one but not onto

    C.

    Onto but not one-to-one

    D.

    Neither one-to-one nor onto

  2. 2.

    If a function f:A→Bf: A \rightarrow B is such that the range of ff is a proper subset of BB, then ff is:

    A.

    An onto function

    B.

    An into function

    C.

    A bijective function

    D.

    A many-to-one function

  3. 3.

    The function f:N→Nf: \mathbb{N} \rightarrow \mathbb{N} defined by f(x)=x2+1f(x) = x^2 + 1 is:

    A.

    Many-to-one and onto

    B.

    One-to-one and onto

    C.

    One-to-one but not onto

    D.

    Many-to-one but not onto

Download the worksheet for Relations and Functions - Types of Functions: One-to-one and Onto functions to practice offline. It includes additional chapter-level practice questions.

Inverse of a Function

Subtopic

Inverse of a Function under Relations and Functions for Grade 12 ICSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Consider the identity function f:R→Rf: \mathbb{R} \rightarrow \mathbb{R} defined by f(x)=xf(x) = x. The inverse function f−1(x)f^{-1}(x) is:

    A.

    −x-x

    B.

    xx

    C.

    1x\frac{1}{x}

    D.

    00

  2. 2.

    If f(x)=x2+5f(x) = \frac{x}{2} + 5, find the value of f−1(x)f^{-1}(x).

    A.

    x−52\frac{x-5}{2}

    B.

    2x−52x - 5

    C.

    x−10x - 10

    D.

    2x−102x - 10

  3. 3.

    For a function f:A→Bf: A \rightarrow B to have an inverse function f−1f^{-1}, what condition must ff satisfy?

    A.

    It must be a bijective function.

    B.

    It must be an injective (one-one) function but not necessarily onto.

    C.

    It must be a surjective (onto) function but not necessarily one-one.

    D.

    It must be an into function.

Download the worksheet for Relations and Functions - Inverse of a Function to practice offline. It includes additional chapter-level practice questions.